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Solving two-level variational inequality. (English) Zbl 0859.90114

Summary: An approach to solving a mathematical program with variational inequality or nonlinear complementarity constraints is presented. It consists in a variational re-formulation of the optimization criterion and looking for a solution of thus obtained variational inequality among the points satisfying the initial variational constraints.

MSC:

90C33 Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming)
49J40 Variational inequalities
93A13 Hierarchical systems
49M30 Other numerical methods in calculus of variations (MSC2010)
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References:

[1] Harker, P.T., Choi, S.-C., ?A penalty function approach for mathematical programs with variational inequality constraints,? Information and Decision Technologies, 17 (1991), pp. 41-50. · Zbl 0732.90075
[2] Smith, M.J., ?A descent algorithm for solving monotone variational inequalities and monotone complementarity problems,? Journal of Optimization Theory and Applications, 44 (1984), pp. 485-496. · Zbl 0535.49023 · doi:10.1007/BF00935463
[3] Outrata, J.V., ?On optimization problems with variational inequality constraints?, SIAM Journal on Optimization, 4 (1994), pp. 340-357. · Zbl 0826.90114 · doi:10.1137/0804019
[4] Karamardian, S., ?An existence theorem for the complementarity problem,? Journal of Optimization Theory and Applications, 18 (1976), pp. 445-454. · Zbl 0304.49026 · doi:10.1007/BF00932654
[5] Eaves, B.C., ?On the basic theorem of complementarity,? Mathematical Programming, 1 (1971), pp. 68-75. · Zbl 0227.90044 · doi:10.1007/BF01584073
[6] Rockafellar, R.T., ?Convex Analysis,? Princeton University Press, Princeton, New Jersey, 1970. · Zbl 0193.18401
[7] Harker, P.T., Pang, J.-S., ?Finite-dimensional variational inequality and nonlinear complementarity problems: a survey of theory, algorithms and applications,? Mathematical Programming, 48 (1990), pp. 161-220. · Zbl 0734.90098 · doi:10.1007/BF01582255
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